Question

A gas has a density of $10$ particles$/m^3$ and a molecular diameter of $0.1$m. What is its mean free path?

• A. $2.25m$
• B. $1m$
  
• C. $3m$
  
• D. $0.25m$
  

Answer 1

The correct option is A $2.25m$

The mean free path estimated by the kinetic theory of gases is given by

$\lambda =\frac{1}{\sqrt{2}\pi n{d}^2}$

Given that number density $n=10{\text{m}}^{-3}$ and diameter $d=0.1\text{m}$

Thus, $\lambda =\frac{1}{\sqrt{2}\pi \times 10\times {0.1}^2}\approx 2.25\text{m}$